Extending the OPGG with the classical reputation mechanism of [1]}, we implement a reputational system adopted by the entire population. After a player cooperates, defects, or abstains from the OPGG, he is assigned a reputation according to the population's social norm. A reputation system requires the definition of a social norm, or reputation dynamics [2]}, that identifies good and bad behaviour. The simplest possible reputational mechanisms are those that assign reputation on the basis of the mere observation of past actions, such as image scoring [3]}.
Arguably, most functional human and animal societies associate the highest reputation to cooperative behaviour. For this reason, we focus our attention to the reputation dynamics that prize cooperation above other actions. Like the binary image score, we simplify the reputation values so that players can have only a good (1), intermediate (0) or bad (-1) reputation, always assigning a good reputation to cooperators. We label the Anti-Defector (AD) norm assigning reputations of -1 to defectors and 0 to loners. Similarly, the Anti-Loner (AL) norm assigns loners a reputation of -1 and defectors a 0. Finally, it is possible to conceptualise norms that do not distinguish between acting as a loner or as a defector. We label these as the Anti-Neither (AN) social norm, which assigns 0 to both actions, and the Anti-Both (AB) social norm, which assigns -1 to both actions. Similar to punishment, reputations update after every OPGG round. We assume that actions are either observed without error or communicated honestly to everyone so that players' resulting reputations are common knowledge within the population.
